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Maxim > Design Support > Technical Documents > Application Notes > Wireless and RF > APP 272 Keywords: rf, rfic, wireless, cellular, cdma, if, oscillator, rfics, IF frequencies, VCO, rf ic

1 Maxim > Design Support > Technical Documents > Application Notes > Wireless and RF > APP 272 Keywords: rf, rfic, wireless, cellular, cdma, if, oscillator, rfics, IF frequencies, VCO, rf ic APPLICATION NOTE 272 IF Tank Design for the MAX2360 Jul 23, 2002 Abstract: This application note presents three voltage-controlled oscillator (VCO) designs for popular IF frequencies of 130MHz, 165MHz, and 380MHz. These designs reduce the number of iterations required for optimized results. Analysis can be accomplished with a simple spreadsheet program. Additional Information Wireless Product Line Page Quick View Data Sheet for the MAX2360/MAX2362/MAX2364 Applications Technical Support Introduction This application note presents three voltage-controlled oscillator (VCO) designs for popular IF frequencies of 130MHz, 165MHz, and 380MHz. These designs reduce the number of iterations required for optimized results. Analysis can be accomplished with a simple spreadsheet program. Click here for an overview of the wireless components used in a typical radio transceiver. VCO Design Figure 2 shows the differential tank circuit used for the MAX2360 IF VCO.For analysis purposes, the tank circuit must be reduced to an equivalent simplified model. Figure 1 depicts the basic VCO model. The frequency of oscillation can be characterized by EQN1: EQN1 f osc = frequency of oscillation L = inductance of the coil in the tank circuit C int = internal capacitance of the MAX2360 tank port C t = total equivalent capacitance of the tank circuit Page 1 of 16

2 Figure 1. Basic VCO model. R n = equivalent negative resistance of the MAX2360 tank port C int = internal capacitance of the MAX2360 tank port C t = total equivalent capacitance of the tank circuit L = inductance of the coil in the tank circuit Figure 2. The MAX2360 tank circuit. Inductor L resonates with the total equivalent capacitance of the tank and the internal capacitance of the oscillator (C t + C int ) (see Figure 1). C coup provides DC block and couples the variable capacitance of the varactor diodes to the tank circuit. C cent is used to center the tank's oscillationfrequency to a nominal value. It is not required but adds a degree of freedom by allowing you to fine-tune resonance between inductor values. Resistors (R) provide reverse-bias voltage to the varactor diodes via the tune voltage line (V tune ). Their value should be chosen large enough so as not to affect loaded tank Q but small enough so that 4kTBR noise is negligible. The resistors' noise voltage gets modulated by K vco, producing phase noise. Capacitance C V is the variable tuning component in the tank. The capacitance of the varactor diode (C V ) is a function of reverse-bias voltage (see Appendix A for the varactor model). V tune is the tuning voltage from a phase-locked loop (PLL). Figure 3 shows the lumped C stray VCO model. Parasitic capacitance and inductance plague every RF circuit. In order to predict the frequency of oscillation, the parasitic elements must be taken into account. The circuit in Figure 3 lumps the parasitic elements in one capacitor called C stray. The frequency of oscillation can be characterized by EQN2: Page 2 of 16

3 EQN2 L = inductance of the coil in the tank circuit C int = internal capacitance of the MAX2360 tank port C cent = tank capacitor used to center oscillation frequency C stray = lumped stray capacitance C coup = tank capacitor used to couple the varactor to the tank C V = net variable capacitance of the varactor diode (including series inductance) C vp = varactor pad capacitance Figure 3. Lumped C stray model. Figure 4 depicts the detailed VCO model. It takes into account the capacitance of the pads but does not include the effects of series inductance for simplicity. C stray is defined as: EQN3 C L = capacitance of the inductor C LP = capacitance of inductor pads C DIFF = capacitance due to parallel traces Figure 4. Detailed VCO model. Page 3 of 16

4 R n = equivalent negative resistance of the MAX2360 tank port C int = internal capacitance of the MAX2360 tank port L T = inductance of series trace to the inductor tank circuit C DIFF = capacitance due to parallel traces L = inductance of the coil in the tank circuit C L = capacitance of the inductor C LP = capacitance of inductor pads C cent = tank capacitor used to center oscillation frequency C coup = tank capacitor used to couple the varactor to the tank C var = variable capacitance of the varactor diode C vp = varactor pad capacitance L S = series inductance of the varactor R = resistance of varactor reverse-bias resistors To simplify analysis, inductance L T is ignored in this design. The effects of L T are more pronounced at higher frequencies. To mathematically model the shift in frequency due to L T with the spreadsheets that follow, the value of C DIFF can be increased appropriately. Minimize inductance L T to prevent undesired series resonance. This can be accomplished by making the traces short. Tuning Gain Tuning gain (K vco ) must be minimized for best closed-loop phase noise. Resistors in the loop filter as well as the resistors "R" (Figure 2) will produce broadband noise. Broadband thermal noise ( ) will modulate the VCO by K vco, which is measured in MHz/V. There are two ways to minimize K vco. One is to minimize the frequency range over which the VCO must tune. The second way is to maximize the tuning voltage available. To minimize the frequency range over which the VCO must tune, tight tolerance components must be used, as will be shown. To maximize tuning voltage, a charge pump with a large compliance range is needed. This is usually accomplished by using a larger V cc. The compliance range for the MAX2360 is 0.5V to Vcc-0.5V. In battery-powered applications, the compliance range is usually fixed by the battery voltage or regulator. Basic Concept for Trimless Design VCO design manufacturability with real-world components will require an error budget analysis. In order to design a VCO to oscillate at a fixed frequency (f osc ), the tolerance of components must be taken into consideration. Tuning gain (K vco ) must be designed into the VCO to account for these component tolerances. The tighter the component tolerance, the smaller the tuning gain and the lower the closedloop phase noise. For the worst-case error budget design, we will look at three VCO models: 1. Maximum-value components (EQN5) 2. Nominal tank, all components perfect (EQN2) 3. Minimum-value components (EQN4) All three VCO models must cover the desired nominal frequency. Figure 5 shows how the three designs must converge to provide a manufacturable design solution. Observations of EQN1 and Figure 5 reveal that minimum-value components shift the oscillation frequency higher, and maximum-value components shift the oscillation frequency lower. Page 4 of 16

5 Figure 5. Worst-case and nominal-tank centering. Minimum tuning range must be used in order to design a tank with the best closed-loop phase noise. Therefore, the nominal tank should be designed to cover the center frequency with overlap to take into account device tolerance. The worst-case high-tune tank and worst-case low-tune tank should tune just to the edge of the desired oscillation frequency. EQN2 can be modified by component tolerance to produce a worst-case high-tune tank EQN4 and worst-case low-tune tank EQN5. EQN4 EQN5 Page 5 of 16

6 T L = % tolerance of inductor (L) T CINT = % tolerance of capacitor (C INT ) T CCENT = % tolerance of capacitor (C CENT ) T CCOUP = % tolerance of capacitor (C COUP ) T CV = % tolerance of varactor capacitance (C V ) EQN4 and EQN5 assume that the strays do not have a tolerance. General Design Procedure Step 1 Estimate or measure pad capacitance and other strays. The stray capacitance on the MAX2360 Rev A EV Kit has been measured with a Boonton Model 72BD capacitance meter. C LP = 0.981pF, C VP = 0.78pF, C DIFF = 0.118pF. Step 2 Determine the value for capacitance C int. This can be found in the MAX2360/MAX2362/MAX2364 Data Sheet on page 5. The typical operating characteristic TANK 1/S11 vs. FREQUENCY shows the equivalent parallel RC values for several popular LO frequencies. Keep in mind that the LO frequency is twice the IF frequency. Example: For an IF frequency of 130MHz, the LO operates at 260MHz. From the 1/s11 chart, R n = -1.66kΩ and C int = 0.31pF. Step 3 Choose an inductor. A good starting point is using the geometric mean. This is an iterative process. EQN6 This equation assumes L in (nh) and C in (pf) (1x10-9 x 1x10-12 = 1x10-21 ). L = 19.3nH for a f osc = MHz. This implies a total tank capacitance C = 19.3pF. An appropriate initial choice for an inductor would be 18nH Coilcraft 0603CS-18NXGBC 2% tolerance. When choosing an inductor with finite step sizes, the following formula EQN6.1 is useful. The total product LC should be constant for a fixed oscillation frequency f osc. EQN6.1 LC = for a f osc = MHz. The trial-and-error process with the spreadsheet in Table1 yielded an inductor value of 39nH 5% with a total tank capacitance of 9.48pF. The LC product for the tank in Figure 6 is , which is close enough to the desired LC product of One can see this is a useful relationship to have on hand. For best phase noise, choose a high Q inductor like the Coilcraft Page 6 of 16

7 0603CS series. Alternatively, a microstrip inductor can be used if the tolerance and Q can be controlled reasonably. Figure MHz IF tank schematic. Step 4 Determine the PLL compliance range. This is the range the VCO tuning voltage (V tune ) is designed to work over. For the MAX2360, the compliance range is 0.5V to V CC -0.5V. For a V CC = 2.7V, this would set the compliance range to 0.5 to 2.2V. The charge-pump output sets this limit. The voltage swing on the tank is 1V P-P centered at 1.6VDC. Even with large values for C coup, the varactor diodes are not forward-biased. This is a condition to be avoided, as the diode rectifies the AC signal on the tank pins, producing undesirable spurious response and loss of lock in a closed-loop PLL. Step 5 Choose a varactor. Look for a varactor with good tolerance over your specified compliance range. Keep the series resistance small. For a figure of merit, check that the self-resonant frequency of the varactor is above the desired operating point. Look at the C V (2.5V)/C V (0.5V) ratio at your voltage compliance range. If the coupling capacitors C coup were chosen large, then the maximum tuning range can be calculated using EQN2. Smaller values of capacitor C coup reduce this effective frequency tuning range. When choosing a varactor, it should have a tolerance specified at your given compliance-range mid and end points. Select a hyperabrupt varactor such as the Alpha SMV for the linear tuning range. Take the value for total tank capacitance, and use that for Cjo of the varactor. Remember that C coup reduces the net capacitance coupled to the tank. Step 6 Pick a value for C coup. Large values of C coup increase the tuning range by coupling more of the varactor in the tank at the expense of decreasing tank loaded Q. Smaller values of C coup increase the effective Q of the coupled varactor and loaded Q of the tank at the expense of reducing the tuning range. Typically this value is chosen as small as possible, while still getting the desired tuning range. Another benefit of choosing a small value for C coup is that it reduces the voltage swing across the varactor diode. This helps thwart forward-biasing the varactor. Page 7 of 16

8 Step 7 Pick a value for C cent, which is usually around 2pF or greater for tolerance purposes. Use C cent to center up the VCO's frequency. Step 8 Iterate with the spreadsheet. MAX2360VCO Tank Designs for IF Frequencies of MHz, 165MHz, and 380MHz The following spreadsheets show designs for several popular IF frequencies for the MAX2360. Keep in mind that the LO oscillates at twice the desired IF frequency. Light grey indicates calculated values Darker grey indicates user input Table MHz IF Tank Design MAX2360 Tank Design and Tuning Range for MHz IF Frequency Total Tank Capacitance vs. V tune V tune Total C Ct (Nominal) Ct (Low) Ct (High) 0.5V Ct high pF pF pF 1.375V Ct mid pF pF pF 2.2V Ct low pF pF pF Tank Components Tolerance C coup 18pF 0.9pF 5% C cent 2.7pF 0.1pF 4% C stray 0.69pF L 39nH 5.00% C int 0.31pF 10.00% Parasitics and Pads (C stray) Due to 0.08pF Q C L Ind. pad C Lp 0.981pF Due to C diff 0.118pF Var. pad C vp 0.78pF Varactor Specs Alpha SMV Cjo 82pF Varactor Tolerance Vj 17V 0.5V 19.00% Page 8 of 16

9 M V 29.00% Cp 0pF 2.5V 35.00% Rs 1Ω Reactance Ls 1.7nH X Ls 2.79 Freq MHz Nominal Varactor X c Net Cap Cv high pF pF Cv mid pF pF Cv low pF pF Negative Tol Varactor (Low Capacitance) Cv high pF pF Cv mid pF pF Cv low pF pF Positive Tol Varactor (High Capacitance) Cv high pF pF Cv mid pF pF Cv low pF pF Nominal LO (Nom) Range Low Tol IF (High) Range Nominal IF (Nom) Range High Tol IF (Low) Range F low MHz MHz MHz MHz F mid MHz MHz MHz MHz F high MHz MHz MHz MHz BW 40.40MHz 27.44MHz 20.20MHz 15.95MHz % BW 15.44% 19.24% 15.44% 13.09% Nominal IF Frequency MHz Design Constraints Condition for bold number <IF =IF > IF Delta Test pass pass pass Raise or lower cent freq by MHz Inc or dec BW MHz Cent adj for min BW MHz K vco 23.77MHz/V Page 9 of 16

10 Figure MHz IF tank schematic. Light grey indicates calculated values Darker grey indicates user input Table MHz IF Tank Design MAX2360 Tank Design and Tuning Range for 165MHz IF Frequency Total Tank Capacitance vs. V tune V tune Total C Ct (Nominal) Ct (Low) Ct (High) 0.5V Ct high pF pF pF 1.375V Ct mid pF pF pF 2.2V Ct low pF pF pF Tank Components Tolerance C coup 18pF 0.9pF 5% C cent 1.6pF 0.1pF 6% C stray 0.62pF L 27nH 5.00% C int 0.34pF 10.00% Page 10 of 16

11 Parasitics and Pads (C stray) Due to C L 0.011pF Q Ind. pad C Lp 0.981pF Due to C diff 0.118pF Var. pad C vp 0.78pF Varactor Specs Alpha SMV Cjo 82pF Varactor Tolerance Vj 17V 0.5V 19.00% M V 29.00% Cp 0pF 2.5V 35.00% Rs 1ohm Reactance Ls 1.7nH X Ls 3.52 Freq MHz Nominal Varactor X c Net Cap Cv high pF pF Cv mid pF pF Cv low pF pF Negative Tol Varactor (Low Capacitance) Cv high pF pF Cv mid pF pF Cv low pF pF Positive Tol Varactor (High Capacitance) Cv high pF pF Cv mid pF pF Cv low pF pF Nominal LO (Nom) Range Low Tol IF (High) Range Nominal IF (Nom) Range High Tol IF (Low) Range F low MHz MHz MHz MHz F mid MHz MHz MHz MHz F high MHz MHz MHz MHz BW 61.07MHz 42.45MHz 30.53MHz 23.74MHz % BW 18.41% 23.22% 18.41% 15.49% Page 11 of 16

12 Nominal IF Frequency 165MHz Design Constraints Condition for bold number < IF = IF > IF Delta Test pass pass pass Raise or lower cent freq by MHz Inc or dec BW MHz Cent adj for min BW MHz K vco 35.92MHz/V Figure MHz IF tank schematic. Light grey indicates calculated values Darker grey indicates user input Table MHz IF Tank Design MAX2360 Tank Design and Tuning Range for 380MHz IF Frequency Total Tank Capacitance vs. V tune V tune Total C Ct (Nominal) Ct (Low) Ct (High) 0.5V Ct high pF pF pF 1.35V Ct mid pF pF pF 2.2V Ct low pF pF pF Page 12 of 16

13 Tank Components Tolerance C coup 15pF 0.8pF 5% C cent 2.4pF 0.1pF 4% C stray 1.42pF L 6.8nH 2.00% C int 0.43pF 10.00% Parasitics and Pads (C stray) Due to C L 0.08pF Q Ind. pad C Lp 0.981pF Due to C diff 0.85pF Var. pad C vp 0.78pF Varactor Specs Alpha SMV Cjo 8.2pF Varactor Tolerance Vj 15V 0.5V 7.50% M V 9.50% Cp 0.67pF 2.5V 11.50% Rs 0.5Ω Reactance Ls 0.8nH X Ls 3.82 Freq MHz Nominal Varactor X c Net Cap C V high pF pF C V mid pF pF C V low pF pF Negative Tol Varactor (Low Capacitance) C V high pF pF C V mid pF pF C V low pF pF Positive Tol Varactor (High Capacitance) C V high pF pF C V mid pF pF C V low pF pF Page 13 of 16

14 Nominal LO (Nom) Range Low Tol IF (High) Range Nominal IF (Nom) Range High Tol IF (Low) Range F low MHz MHz MHz MHz F mid MHz MHz MHz MHz F high MHz MHz MHz MHz BW 70.00MHz 36.41MHz 35.00MHz 33.74MHz % BW 9.06% 9.11% 9.06% 9.03% Nominal IF Frequency 380MHz Design Constraints Condition for bold number < IF = IF > IF Delta Test pass pass pass Raise or lower cent freq by MHz Inc or dec BW MHz Cent adj for min BW MHz K vco Appendix A 41.18MHz/V Figure 9. Varactor model. Alpha Application Note AN1004 has additional information on varactor models. Varactor capacitance is defined in EQN7. EQN7 Page 14 of 16

15 Alpha SMV Alpha SMV C jo = 82 pf C jo = 8.2 pf V j =17 V V j =15 V M = 14 M = 9.5 C p = 0 C p = 0.67 R s = 1Ω R s = 0.5Ω L s = 1.7 nh L s = 0.8 nh The series inductance of the varactor is taken into account by backing out the inductive reactance and calculating a new effective capacitance C V. EQN8 References 1. Chris O'Connor, Develop Trimless Voltage-Controlled Oscillators, Microwaves and RF, July Wes Hayward, Radio Frequency Design, Chapter Krauss, Bostian, Raab, Solid State Radio Engineering, Chapters 2, 3, Alpha Industries Application Note AN Coilcraft, RF Inductors Catalog, March 1998, p Maxim, MAX2360/MAX2362/MAX2364 Data Sheet Rev Maxim, MAX2360 Evaluation Kit Data Sheet Rev 0. Related Parts MAX2360 Complete Dual-Band Quadrature Transmitters MAX2361 Complete Dual-Band Quadrature Transmitters MAX2362 Complete Dual-Band Quadrature Transmitters MAX2363 Complete Dual-Band Quadrature Transmitters MAX2364 Complete Dual-Band Quadrature Transmitters MAX2365 Complete Dual-Band Quadrature Transmitters Page 15 of 16

16 More Information For Technical Support: For Samples: Other Questions and Comments: Application Note 272: APPLICATION NOTE 272, AN272, AN 272, APP272, Appnote272, Appnote 272 Copyright by Maxim Integrated Products Additional Legal Notices: Page 16 of 16

Introduction. Keywords: rf, rfdesign, rfic, vco, rfics, rf design, rf ics. APPLICATION NOTE 530 VCO Tank Design for the MAX2310.

Introduction. Keywords: rf, rfdesign, rfic, vco, rfics, rf design, rf ics. APPLICATION NOTE 530 VCO Tank Design for the MAX2310. Maxim > Design Support > Technical Documents > Application Notes > Wireless and RF > APP 530 Keywords: rf, rfdesign, rfic, vco, rfics, rf design, rf ics APPLICATION NOTE 530 VCO Tank Design for the MAX2310